fix Postgres diagnose conn handling

[eric-weaver]

What does this PR do?

• Fixes a potential connection leak when PostgreSql._new_connection() successfully opens a connection but then fails to configure the connection with our expected initialization SET commands.
• Fixes surfacing connection errors in diagnose.py when opening a connection and receives an authentication error from AWS or Azure managed providers.

Motivation

Follow up from #23433

Review checklist (to be filled by reviewers)

• Feature or bugfix MUST have appropriate tests (unit, integration, e2e)
• Add the qa/skip-qa label if the PR doesn't need to be tested during QA.
• If you need to backport this PR to another branch, you can add the backport/<branch-name> label to the PR and it will automatically open a backport PR once this one is merged

[datadog-prod-us1-3]

🎉 All green!

❄️ No new flaky tests detected
🧪 All tests passed

🎯 Code Coverage (details)
• Patch Coverage: 100.00%
• Overall Coverage: 92.99% (+5.76%)

_{This comment will be updated automatically if new data arrives.
🔗 Commit SHA: 803331a | Docs | Datadog PR Page | Give us feedback!}

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 89.39%. Comparing base (0e82485) to head (803331a).
⚠️ Report is 9 commits behind head on master.

Additional details and impacted files

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[joelmarcotte]

@codex review

[dd-octo-sts]

Validation Report

All 20 validations passed.

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[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. Keep it up!

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